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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The Trotter-Kato theorem and approximation of PDEs
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by Kazufumi Ito and Franz Kappel PDF
Math. Comp. 67 (1998), 21-44 Request permission

Abstract:

We present formulations of the Trotter-Kato theorem for approximation of linear C${}_0$-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes’ equation as illustrative examples.
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Additional Information
  • Kazufumi Ito
  • Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
  • Email: kito@eos.ncsu.edu
  • Franz Kappel
  • Affiliation: Institut für Mathematik, Universität Graz, Heinrichstraße 36, A8010 Graz, Austria
  • Email: franz.kappel@kfunigraz.ac.at
  • Received by editor(s): August 18, 1995
  • Received by editor(s) in revised form: August 1, 1996
  • Additional Notes: Research of the first author was supported in part by the NSF under Grant UINT-8521208 and DMS-8818530 and by the Air Force Office of Scientific Research under contract AFOSR-90-0091.
    Research by the second author was supported in part by FWF(Austria) under Grants P6005, P8146-PHY and under F003.
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 21-44
  • MSC (1991): Primary 47D05, 47H05, 65J10, 35K22, 35L99
  • DOI: https://doi.org/10.1090/S0025-5718-98-00915-6
  • MathSciNet review: 1443120